Details

sample152.0ms

Algorithm

intervals

Results

63.0ms	65×	body	2560	valid
23.0ms	39×	body	1280	valid
23.0ms	57×	body	80	valid
16.0ms	39×	body	640	valid
13.0ms	38×	body	320	valid
4.0ms	18×	body	160	valid

simplify29.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 2 expressions with local error:

18.5b	(/ (- 1 (cos x)) (* x x))
1.9b	(- 1 (cos x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 47

Calls

2 calls:

Slowest

35.0ms	(/ (- 1 (cos x)) (* x x))
5.0ms	(- 1 (cos x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

60.0ms	(/ (- 1 (cos x)) (* x x))
28.0ms	(- 1 (cos x))

simplify2.5s

Counts: 53 → 53

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

18.4b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.3b	(+ 1 (cos x))
0.2b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity`
22×	`times-frac`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`flip3-+` `flip-+` `insert-posit16` `div-inv`
3×	`div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

Slowest

40.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
14.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
10.0ms	(* (sin x) (sin x))
7.0ms	(+ 1 (cos x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
57.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
32.0ms	(* (sin x) (sin x))
17.0ms	(+ 1 (cos x))

simplify651.0ms

Counts: 127 → 127

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (tan (/ x 2)) x)
0.1b	(/ (sin x) x)
0.1b	(* (/ (sin x) x) (/ (tan (/ x 2)) x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 108

Calls

3 calls:

Slowest

20.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
10.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series262.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

140.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
71.0ms	(/ (tan (/ x 2)) x)
51.0ms	(/ (sin x) x)

simplify1.8s

Counts: 117 → 117

prune929.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sin x) (/ (tan (/ x 2)) x))
0.1b	(/ (tan (/ x 2)) x)
0.0b	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`times-frac`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
6×	`cbrt-undiv` `associate-/r*` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`associate-l` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr` `associate-/l/`
1×	`pow-prod-down` `tan-quot` `*-commutative`

Counts

3 → 87

Calls

3 calls:

Slowest

17.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
17.0ms	(* (sin x) (/ (tan (/ x 2)) x))
9.0ms	(/ (tan (/ x 2)) x)

series300.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

119.0ms	(* (sin x) (/ (tan (/ x 2)) x))
108.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
72.0ms	(/ (tan (/ x 2)) x)

simplify2.8s

Counts: 96 → 96

prune773.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	1627×	body	2560	valid
1.1s	1425×	body	640	valid
964.0ms	1227×	body	1280	valid
366.0ms	922×	body	320	valid
283.0ms	2321×	body	80	valid
135.0ms	478×	body	160	valid